# Ex 5.1, 10 - Chapter 5 Class 12 Continuity and Differentiability

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Ex 5.1, 10 Find all points of discontinuity of f, where f is defined by = +1, 1 & 2+1 , <1 We have = +1, 1 & 2+1 , <1 Case 1: At x = 1 f is continuous at x = 1 y L.H.L = R.H.L = 1 i.e. lim x 1 = lim x 1 + = 1 = +1 1 =1+1 = 2 Thus, L.H.L = R.H.L = 1 f is continuous at x = 1 Case 2 Let x = c (where c < 1) = 2 +1 f is continuous at x = c if if lim x = ( ) Thus , lim x = ( ) f is continuous for = ( c is less than 1 ) f is continuous for all real numbers less than 1. Case 3 Let x = c (where c > 1) = +1 f is continuous at x = c if lim x = ( ) Thus lim x = ( ) f is continuous at = ( c is less than 1) f is continuous at all real numbers less than 1 Hence, there is no point of discontinuity f is continuous at all real point. Thus, f is continuous for all .

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.